A relativistic framework to establish Coordinate time on the Moon and Beyond

Published

February 17, 2024

Author(s)

Neil Ashby, Bijunath Patla

Abstract

The rate of clocks, according to Einstein's theory of relativity, is influenced by the gravitational potential and relative motion of the clocks. A grid of synchronized clocks that is traceable to an ideal clock at a predetermined point in space is the basis of a coordinate time reference for comparing local time variations of clocks due to gravitational and motional effects. As humanity aspires to explore the solar system and investigate distant worlds such as the Moon, Mars, and beyond, there is a growing need to establish and broaden coordinate time references. We present a relativistic framework and discuss a coordinate time for the Moon and its relationship with time on Earth as determined by standard clocks on the geoid. Using this framework, we also calculate the clock rates at earth-moon Lagrange points. Recognizing the rate differences among coordinate times across celestial bodies and stable points, particularly for orbiters at Lagrange points, is crucial for establishing reliable communication infrastructure. This understanding also underpins precise navigation in cislunar space and on the surfaces of celestial bodies, and thus playing a pivotal role in ensuring the interoperability of various position, navigation, and timing (PNT) systems extending the far reaches of the inner solar system.

Citation

Nature Communications

Pub Type

Journals

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Keywords

Relativity, Moon, Time, clocks, precision metrology

Citation

Ashby, N. and Patla, B. (2024), A relativistic framework to establish Coordinate time on the Moon and Beyond, Nature Communications, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=957328 (Accessed April 30, 2025)